1. The Prophet Muhammad (SAWA) himself use to celebrate his birth by fasting every Monday being the day of his birth.
The Infallible Imams used to celebrate and encourage the believers to celebrate through performing recommended deeds and acts on the day of the birth anniversary like fasting, performing Ghusl, Ziyarat etc.
2. We do not have any evidence on celebrating the birthday of children or adults except of the Infallible and great personalities with them.